Shane's engagement ring is not the same one Oliver gave her when he proposed at the end of the last movie. In the 3 years between filming the last movie and this one, the ring was lost, and because it was an antique ring they couldn't get a replacement. The rings shown in the closeups at the wedding are Kristen Booth's own rings.
The blondness of Shane/Kristen's hair goes back and forth throughout the movie.
Oliver tells Shane's mom that he planted the roses for Shane that were the same kind that she had at her childhood home. But Oliver wasn't the one who planted them; he gave Shane a cutting from the rose bush at the site of her old home, but later Shane told Oliver she planted them.
Owen's clinical trial started on the same day as Oliver and Shane's wedding, which they say multiple times is on a Saturday. But a clinical trial would never start on a weekend because if something goes wrong hospitals have their least-experienced staff working on the weekends. Also, the staff running the clinical trial would likely not be working on a Saturday.
Charlie was brought in as a temp so that the DLO wouldn't fall behind the workload while Shane and Oliver are on their honeymoon. However, Charlie had her baby before Shane and Oliver's wedding, and nothing was said in this movie or the next, who did end up helping in the DLO while Oliver and Shane were gone. And just 10 weeks earlier, based on information given in the next movie, it's never said who helped out when Norman and Rita were on their honeymoon. And if no one did, they would have fallen behind already.